Data

We used data from the 2016 ACS for Puerto Rico to examine wage gaps between individuals with different education levels. Our research questions are: 1) How do earnings vary by education level? 2) How does the premium for education vary by gender? The 2016 ACS is a nationally representative sample of 5194. The household survey includes questions pertaining to each household member’s demographic characteristics and labor market activity.

We restrict our sample to these three racial groups: White, Black and Other. In addition, given our goal of examining earning differences by gender and marital status and the reporting of earnings in the ACS on an annual basis (wages, salary, commissions, bonuses, tips, and self-employment income during the past 12 months), we restrict our sample to full-time year-round (FTYR) workers. We define FTYR workers as individuals who report positive earnings over the past year, who worked at least 40 of the past 52 weeks, and who worked at least 35 hours per week in a usual work week over this period.

EDA Insights:

For our exploratory analysis we looked at population breakdowns by education, age, marital status, gender, race, earnings, and work hours. We applied filters on education (HS diploma or above), age (18-64), and work hours (>35/week).

An earnings histogram identified a default maximum amount of earnings (189k) which we also filtered out of the data. The earning distribution is progressive above the median, but drops off sharply below the median, likely indicating the presence of a minimum wage. The correlation between age and earnings is very weak (.23). Likewise, earnings is very weakly correlated with hours worked among those who work more than 35 hours per week. However, white individuals appear to have an earnings premium over other races, and both married and divorced individuals appear to have an earnings premium over those who have never been married. Given that the correlation between age and earnings was weak, this may be due to other qualitative factors possessed by those who get married. Married was recategoried to married and not married.

Earnings appear positively correlated with how well people speak English, as well as with higher levels of education. It should be noted that, on the island, fluency in the English language is neither a requirement, nor really needed. As a Latin American destination, the predominant language spoken and used (e.g. street signs, day-to-day communications) is Spanish, with English only coming into use in the tourism industry, or in those industies or companies imported from the mainland. This may help to explain the earning difference, as those are likely to pay more than local businesses (note that tourism is the largest industry on the island and the source of most of the island’s GDP). Men also appear to earn a small premium over women.

The age distribution of full time workers is skewed towards older adults, possibly indicating that younger workers have trouble finding full-time work, wait to enter the workforce, or are leaving the territory.

Task 1:

Examine the first 10 or 20 observations (rows of data) corresponding to variables of interest (columns) and compare the observed values to the data dictionary for person records.

Earnings Sex Age Race Marital Status Education Work Week Work Hours
34000 Male 47 White Married Associate’s degree 50 to 52 40
13000 Male 58 Black or African American Never married High school diploma 50 to 52 40
18000 Male 50 White Married Master’s degree 50 to 52 40
10300 Female 39 White Married Bachelor’s degree 50 to 52 40
28600 Female 39 Black or African American Married Bachelor’s degree 50 to 52 45
24800 Male 37 Black or African American Married Bachelor’s degree 50 to 52 46
22000 Female 47 Some Other Never married Associate’s degree 50 to 52 40
19000 Female 60 Black or African American Never married High school diploma 50 to 52 40
87000 Female 58 White Divorced Associate’s degree 50 to 52 40
22900 Male 61 White Divorced High school diploma 50 to 52 40
19000 Male 39 Black or African American Married Associate’s degree 50 to 52 38
19600 Female 36 Black or African American Married Bachelor’s degree 50 to 52 40
48000 Male 30 Two or More Races Divorced Some college 50 to 52 40
40000 Female 30 White Never married Some college 50 to 52 40
15600 Female 41 White Never married High school diploma 50 to 52 40
12100 Male 46 White Divorced High school diploma 50 to 52 40
14000 Male 53 White Married High school diploma 50 to 52 40
80000 Male 38 White Never married Bachelor’s degree 50 to 52 40
15100 Female 26 Some Other Never married High school diploma 50 to 52 40
84000 Female 60 White Married Doctorate degree 50 to 52 40

Task 2:

Compute and examine descriptive statistics including the minimum, maximum, mean, and median for quantitative variables of interest

Total person’s earnings

ss16ppr (N = 5,194)
Minimum 10000.00
Maximum 125000.00
Median 24000.00
Mean 29278.84

Age

ss16ppr (N = 5,194)
Minimum 18.00
Maximum 64.00
Median 43.00
Mean 29278.84

Hours worked

ss16ppr (N = 5,194)
Minimum 35.00000
Maximum 99.00000
Median 40.00000
Mean 41.21544

Race: White

In Puerto Rico, the majority of people identify themselves as white. Minority races including American Indian, Alaska Native, Asian, Native Hawaiian and Other Pacific Islander can be eliminated.

RACWHT Count
No 1401
Yes 3793

Race: Black

RACBLK Count
No 4417
Yes 777

Race: Other

RACOTHER Count
No 4381
Yes 813

Marital status

MAR Count
Married 2580
Widowed 65
Divorced 944
Separated 105
Never married 1500
MAR1 Count
No 2614
Yes 2580
MAR2 Count
Married 2645
Divorced 1049
Never married 1500

Educational attainment

SCHL Count
High school diploma 1148
Some college 791
Associate’s degree 818
Bachelor’s degree 1726
Master’s degree 505
Professional degree 113
Doctorate degree 93

Sex

SEX Count
Male 2627
Female 2567

Task 3:

Generate and examine histograms for quantitative variables of interest

Total person’s earnings

Age

Hours worked

Task 4:

Generate and examine bar charts/graphs for qualitative variables of interest

Race

Race: White

Race: Black

Race: Other

Marital Status

Educational attainment

Sex

Gender is nearly equalized in Puerto Rico

Work week

Task 5:

Generate and examine cross tabulations, scatterplots, and/or correlation coefficients of interest

Age vs. Total person’s earnings

The correlation of 0.22 for age and earnings indicates a very weak relationship. Age is neither a primary reason for differences in earnings, nor a clear proxy for some other variable.

Work hours vs. Total person’s earnings

The correlation of 0.18 for earnings and work hours is also very weak. No doubt it would be strong if the data were not filtered to those working more than 35 hours per week. Interestingly, earnings appear to drop for those working more than 60 hours per week.

Race: White

RACWHT: No (N = 1,401) RACWHT: Yes (N = 3,792)
Minimum 10000 10000
Maximum 96000 100000
Median 23000 24600
Mean 26946.56 30115.28

Race: Black

RACBLK: No (N = 4,417) RACBLK: Yes (N = 776)
Minimum 10000 10000
Maximum 98000 100000
Median 24000 23000
Mean 29550.70 27608.03

Race: Other

RACOTHER: No (N = 4,380) RACOTHER: Yes (N = 813)
Minimum 10000 10000
Maximum 100000 96000
Median 24000 23600
Mean 29638.67 27222.51

Marital Status

MAR1: No (N = 2,614) MAR1: Yes (N = 2,579)
Minimum 10000 10000
Maximum 100000 98000
Median 22000 25600
Mean 27036.95 31514.04

Educational attainment

SCHL: High school diploma (N = 1,147) SCHL: Some college (N = 791) SCHL: Associate’s degree (N = 818) SCHL: Bachelor’s degree (N = 1,726) SCHL: Master’s degree (N = 505) SCHL: Professional degree (N = 113) SCHL: Doctorate degree (N = 93)
Minimum 10000 10000 10000 10000 10000 10400 17900
Maximum 90000 93000 90000 98000 98000 100000 96000
Median 18000 20000 20950 29200 35000 46000 60000
Mean 21948.24 24662.63 25150.86 32669.99 38262.18 49146.90 58373.12

Preliminary Econometric Estimates

First Model:

\[Earning = \beta_0 + Divorced * \beta_1 + NeverMarried * \beta_2 + Female * \beta_3 + RaceBlack * \beta_4 + RaceOther * \beta_5 + SomeCollege * \beta_6 + Associate * \beta_7 + Bachelor * \beta_8 + Master * \beta_9 + Professional * \beta_10 + Doctoral * \beta_11 + Age * \beta_12\]

## 
## Call:
## lm(formula = PERNP ~ Divorced + NeverMarried + Female + RaceBlack + 
##     RaceOther + SomeCollege + Associate + Bachelor + Master + 
##     Professional + Doctoral + AGEP, data = ss16ppr)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -43686  -9198  -2921   5348  63456 
## 
## Coefficients:
##              Estimate Std. Error t value             Pr(>|t|)    
## (Intercept)  12519.82    1104.43  11.336 < 0.0000000000000002 ***
## Divorced     -1146.91     546.10  -2.100             0.035760 *  
## NeverMarried -2959.79     517.30  -5.722       0.000000011144 ***
## Female       -4824.55     429.48 -11.234 < 0.0000000000000002 ***
## RaceBlack    -1301.52     589.11  -2.209             0.027196 *  
## RaceOther    -2132.00     577.36  -3.693             0.000224 ***
## SomeCollege   4311.57     691.75   6.233       0.000000000494 ***
## Associate     4232.24     685.40   6.175       0.000000000713 ***
## Bachelor     12406.91     584.22  21.237 < 0.0000000000000002 ***
## Master       17855.61     808.79  22.077 < 0.0000000000000002 ***
## Professional 28203.02    1469.19  19.196 < 0.0000000000000002 ***
## Doctoral     35732.87    1609.22  22.205 < 0.0000000000000002 ***
## AGEP           285.13      20.95  13.609 < 0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 14860 on 5180 degrees of freedom
## Multiple R-squared:  0.2484, Adjusted R-squared:  0.2467 
## F-statistic: 142.7 on 12 and 5180 DF,  p-value: < 0.00000000000000022
  • Coefficients Explanation
    • Holding gender, race, education and age constant, married or widowed people makes $1146.91 more than people who divorced or separated on average.
    • Holding gender, race, education and age constant, married or widowed people makes $2959.79 more than people who never married on average.
    • Holding marriage, race, education and age constant, male makes $4824.55 more than female on average.
    • Holding marriage, gender, education and age constant, White makes $1301.52 more than Black on average.
    • Holding marriage, gender, education and age constant, White makes $2132 more than Other race on average.
    • Holding marriage, gender, race and age constant, people have high school education makes $4311.57 less than people have some college education on average.
    • Holding marriage, gender, race and age constant, people have high school education makes $4232.24 less than people have associate education on average.
    • Holding marriage, gender, race and age constant, people have high school education makes $12406.91 less than people have bachelor’s degree on average.
    • Holding marriage, gender, race and age constant, people have high school education makes $17855.61 less than people have master’s degree on average.
    • Holding marriage, gender, race and age constant, people have high school education makes $28203.02 less than people have Professional education on average.
    • Holding marriage, gender, race and age constant, people have high school education makes $35732.87 less than people have doctor’s degree on average.
    • Holding marriage, gender, race and education constant, people make $285.13 more as age increases on average between the age of 18 to 64.

Second Model:

\[Earning = \beta_0 + Female * \beta_1 + SomeCollege * \beta_2 + Associate * \beta_3 + Bachelor * \beta_4 + Master * \beta_5 + Professional * \beta_6 + Doctoral * \beta_7\]

## 
## Call:
## lm(formula = PERNP ~ Female + SomeCollege + Associate + Bachelor + 
##     Master + Professional + Doctoral, data = ss16ppr)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -38660  -9524  -3508   5802  67102 
## 
## Coefficients:
##              Estimate Std. Error t value             Pr(>|t|)    
## (Intercept)   23324.4      471.0  49.521 < 0.0000000000000002 ***
## Female        -4656.1      440.7 -10.566 < 0.0000000000000002 ***
## SomeCollege    3339.6      711.0   4.697          0.000002704 ***
## Associate      4000.8      705.6   5.670          0.000000015 ***
## Bachelor      12229.4      601.2  20.343 < 0.0000000000000002 ***
## Master        17934.3      832.9  21.532 < 0.0000000000000002 ***
## Professional  28336.0     1515.3  18.700 < 0.0000000000000002 ***
## Doctoral      37602.1     1656.5  22.699 < 0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15330 on 5185 degrees of freedom
## Multiple R-squared:  0.1989, Adjusted R-squared:  0.1979 
## F-statistic:   184 on 7 and 5185 DF,  p-value: < 0.00000000000000022
  • Coefficients Explanation
    • Holding education constant, male makes $4656 more than female on average.
    • Holding gender constant, people have high school education makes $4311.57 less than people have some college education on average.
    • Holding gender constant, people have high school education makes $4232.24 less than people have associate education on average.
    • Holding gender constant, people have high school education makes $12406.91 less than people have bachelor’s degree on average.
    • Holding gender constant, people have high school education makes $17855.61 less than people have master’s degree on average.
    • Holding gender constant, people have high school education makes $28203.02 less than people have Professional education on average.
    • Holding gender constant, people have high school education makes $35732.87 less than people have doctor’s degree on average.